In order to restrict greenhouse gases emissions, CO2 should be captured from the postcombustion gas for further treatment, for example, geosequestration. In this work, the separation performance of the two-stage membrane system with a recycle stream was investigated using the cross-flow model. For larger CO2/N-2 selectivities that can be achieved in the lab, for example, selectivity of 52, the separation target of CO2 purity > 95% and CO2 recovery > 90% can be fulfilled by the two-stage system. The process cost of the two-stage membrane process was investigated. There is an optimum pressure ratio with which the capital cost and the energy cost can be balanced to minimize the total cost. Using the optimum pressure ratios and efficient membranes, the total cost of the two-stage system can be reduced to a range that is competitive with the process cost of the traditional chemical absorption method. For example, with feed compression applied, the total cost of the two-stage membrane system using the membrane with CO2/N-2 selectivity of 52 and CO2 permeance of 3.12 x 10(-3) m(3) (STP) m(-2).s(-1) MPa-1 is estimated to be $47.9/(ton CO2 recovered).